Thread: Is my answer correct?

Question: Evaluate limx->0 [(1/3+x)-(1/3) / (x)]
Possible answers:
a) -1/9
b) 0
c) 1/9
d) does not exist

I believe the answer is a. Is this right?
Any help is appreciated.

That's correct.

Assuming that you mean lim(x->0) (1/(3+x))-(1/3))/x (notice the additional parentheses), then, yes, 1/9 is correct.

But I first interpreted his as lim(x->0) ((1/3)+ x)- (1/3))/x and that has a limit of 1. Which did you mean?